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White Noise Calculus and Fock Space

  • Book
  • © 1994

Overview

Authors:
  1. Nobuaki Obata
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1577)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-x
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  2. Prerequisites

    • Nobuaki Obata
    Pages 1-18

  3. White noise space

    • Nobuaki Obata
    Pages 19-32

  4. White noise functionals

    • Nobuaki Obata
    Pages 33-70

  5. Operator theory

    • Nobuaki Obata
    Pages 71-108

  6. Toward harmonic analysis

    • Nobuaki Obata
    Pages 109-150

  7. Addendum

    • Nobuaki Obata
    Pages 151-166

  8. Back Matter

    Pages 167-186
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Keywords

About this book

White Noise Calculus is a distribution theory on Gaussian space, proposed by T. Hida in 1975. This approach enables us to use pointwise defined creation and annihilation operators as well as the well-established theory of nuclear space.This self-contained monograph presents, for the first time, a systematic introduction to operator theory on fock space by means of white noise calculus. The goal is a comprehensive account of general expansion theory of Fock space operators and its applications. In particular,first order differential operators, Laplacians, rotation group, Fourier transform and their interrelations are discussed in detail w.r.t. harmonic analysis on Gaussian space. The mathematical formalism used here is based on distribution theory and functional analysis , prior knowledge of white noise calculus is not required.

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